The double CFTP method

We consider the problem of the exact simulation of random variables Z that satisfy the distributional identity Z L = V Y + (1 − V )Z, where V ∈ [0, 1] and Y are independent, and L = denotes equality in distribution. Equivalently, Z is the limit of a Markov chain driven by that map. We give an algorithm that can be automated under the condition that we have a source capable of generating independent copies of Y , and that V has a density that can be evaluated in a black box format. The method uses a doubling trick for inducing coalescence in coupling from the past. Applications include exact samplers for many Dirichlet means, some two-parameter Poisson–Dirichlet means, and a host of other distributions related to occupation times of Bessel bridges that can be described by stochastic fixed point equations. Keywords and phrases. Random variate generation. Perpetuities. Coupling from the past. Random partitions. Stochastic recurrences. Stochastic fixed point equations. Distribution...

• Type: Journal
• Year: 2011
• Where: TOMACS
• Authors: Luc Devroye, Lancelot F. James
• Keywords: Hong Kong, Markov Chain, Monte Carlo, TOMACS 2011